A247330 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (2 + A(x)^n)^n.

1, 3, 12, 75, 633, 6330, 70410, 845490, 10778385, 144342129, 2016502329, 29249703273, 439097183598, 6807064047249, 108811265375748, 1791748638013341, 30373586425246566, 529855701281428431, 9509268033398381151, 175539561089425403601, 3332349856995500161920, 65037265540406292591147

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f. satisfies: A(x) = Sum_{n>=0} x^n * A(x)^(n^2)/(1 - 2*x*A(x)^n)^(n+1).

Example

G.f.: A(x) = 1 + 3*x + 12*x^2 + 75*x^3 + 633*x^4 + 6330*x^5 + 70410*x^6 +...
where the g.f. satisfies following series identity:
A(x) = 1 + x*(2+A(x)) + x^2*(2+A(x)^2)^2 + x^3*(2+A(x)^3)^3 + x^4*(2+A(x)^4)^4 + x^5*(2+A(x)^5)^5 + x^6*(2+A(x)^6)^6 +...
A(x) = 1/(1-2*x) + x*A(x)/(1-2*x*A(x))^2 + x^2*A(x)^4/(1-2*x*A(x)^2)^3 + x^3*A(x)^9/(1-2*x*A(x)^3)^4 + x^4*A(x)^16/(1-2*x*A(x)^4)^5 + x^5*A(x)^25/(1-2*x*A(x)^5)^6 + x^6*A(x)^36/(1-2*x*A(x)^6)^7 +...

Prog

(PARI) {a(n, t=2)=local(A=1+x); for(i=1, n, A=sum(k=0, n, A^(k^2)*x^k/(1 - t*A^k*x +x*O(x^n))^(k+1) )); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
(PARI) {a(n, t=2)=local(A=1+x); for(i=1, n, A=sum(k=0, n, x^k * (t + A^k +x*O(x^n))^k)); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A203000, A247331.

Sequence in context: A291951 A176408 A238630 * A168366 A134524 A120591

Adjacent sequences: A247327 A247328 A247329 * A247331 A247332 A247333

Keyword

nonn

Author

Paul D. Hanna, Sep 13 2014

Status

approved